Wood (2-3) claimed his second straight victory after beginning the season winless in six starts. The Chicago left-hander scattered five hits while walking one and striking out six.
Joe Mather's homer in the fourth inning broke a scoreless tie and the Cubs put the game away with four runs in the seventh, scoring on errors by Mets right fielder Lucas Duda and second baseman Ronny Cedeno.
Jeff Baker and Geovany Soto added RBI in the big frame, which helped break a four-game Cubs losing streak.
The Mets' Johan Santana (5-4) was saddled with the loss after yielding a pair of runs on five hits over six full frames.
Ike Davis went deep for New York.
Swim Week Miami Beach 2014 [PHOTOS]